# Polar Coordinates

• May 6th 2010, 09:30 AM
Ricko
Polar Coordinates
Let $(x,y)$ be the common coordinates of $R^{2}$ and $V=R^{2}-\{(x,0):x\le 0\}$. On $V$ the polar coordinates are defined unambiguously for $0<\theta<2\pi$. Find $\frac{\partial}{\partial{r}}$, $\frac{\partial}{\partial{\theta}}$. Find the relationship between these vectors and $\frac{\partial}{\partial{x}}|$, $\frac{\partial}{\partial{y}}|$.
• May 7th 2010, 03:43 AM
HallsofIvy
Quote:

Originally Posted by Ricko
Let $(x,y)$ be the common coordinates of $R^{2}$ and $V=R^{2}-\{(x,0):x\le 0\}$. On $V$ the polar coordinates are defined unambiguously for $0<\theta<2\pi$. Find $\frac{\partial}{\partial{r}}$, $\frac{\partial}{\partial{\theta}}$. Find the relationship between these vectors and $\frac{\partial}{\partial{x}}|$, $\frac{\partial}{\partial{y}}|$.

1. By "common coordinates" I think you mean "Cartesian Coordinates"

2. I don't know what the "|" is in $\frac{\partial }{\partial x}|$ and $\frac{\partial }{\partial y}|$

3. If you mean the partial derivatives, use the chain rule: $\frac{\partial U}{\partial r}= \frac{\partial x}{\partial r}\frac{\partial U}{\partial x}+ \frac{\partial y}{\partial r}\frac{\partial U}{\partial y}$.
• May 7th 2010, 11:16 AM
Drexel28
Quote:

Originally Posted by HallsofIvy
1. By "common coordinates" I think you mean "Cartesian Coordinates"

2. I don't know what the "|" is in $\frac{\partial }{\partial x}|$ and $\frac{\partial }{\partial y}|$

3. If you mean the partial derivatives, use the chain rule: $\frac{\partial U}{\partial r}= \frac{\partial x}{\partial r}\frac{\partial U}{\partial x}+ \frac{\partial y}{\partial r}\frac{\partial U}{\partial y}$.

Isn't common coordinates a reference to overlap maps?